Question: Our club has 10 members, and wishes to pick a president, secretary, treasurer, and morale officer.  In how many ways can we choose the officers, if individual members can only hold at most one office?
The president can be any of the 10 members, the secretary can be any of the 9 remaining members, the treasurer can be any of the remaining 8 members, and the morale officer can be any of the remaining 7 members. There are $10\times 9\times 8\times7=\boxed{5,\!040}$ ways.